cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A097484 Write the odd positive integers on labels in numerical order, forming an infinite sequence L. Consider the succession of single digits of L: 1 3 5 7 9 1 1 1 3 1 5 1 7 1 9 2 1 2 3 2 5 2 7 2 9 3 1 ... (A031312). This sequence is a derangement of L that produces the same succession of digits, subject to the constraint that the smallest unused label must be used that does not lead to a contradiction.

Original entry on oeis.org

13, 5, 7, 9, 1, 113, 15, 17, 19, 21, 23, 25, 27, 29, 3, 133, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 11, 1113, 115, 117, 119, 121, 123, 125, 127, 129, 131
Offset: 1

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Author

Eric Angelini, Sep 19 2004

Keywords

Comments

Derangement here means the n-th element of L is not the n-th element of this sequence, so a(n) != 2n - 1.

Examples

			We must begin with 1,3,5,7... and we cannot have a(1) = 1, so the next possibility is the label "13". The next term must be the smallest available label not leading to a contradiction, thus "5". The next one will be "7", etc. After the label "9" the smallest available label is "1". After this "1" we cannot have a(6) = 11 -- we thus take the smallest available label which is "113". No label is allowed to start with a leading zero.

Crossrefs

Cf. A005408, A097481, A097485, A097487, A097488, A097500, A097912, A097962, A098067, A098080.
Same type of sequence -- but for even numbers -- is A097481. - Eric Angelini, Aug 12 2008

Extensions

Corrected and extended by Jacques ALARDET and Eric Angelini, Aug 12 2008
Derangement wording introduced by Danny Rorabaugh, Nov 26 2015

A105967 Slowest increasing sequence all of whose successive digits are the digits of the Fibonacci numbers.

Original entry on oeis.org

0, 11, 23, 58, 132, 134, 558, 914, 4233, 3776, 10987, 15972, 58441, 81676, 510946, 1771128, 6574636, 8750251, 21393196, 41831781, 151422983, 204013462
Offset: 0

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Author

Alexandre Wajnberg, Apr 28 2005

Keywords

Links

Crossrefs

Cf. A093086, A102085, A098080.

Formula

Write down the Fibonacci numbers and consider it as a unique succession of digits. Divide up into chunks of minimal length (and not beginning with 0) so that chunks are increasing numbers in order to form the slowest ever increasing sequence of slices (disregarding the number of digits) of the succession of the digits of the Fibonacci numbers.

A097473 Slowest ever increasing sequence in which all successive digits are the digits of the Fibonacci sequence.

Original entry on oeis.org

0, 11, 23, 58, 132, 134, 558, 914, 4233, 377610, 987159, 7258441, 81676510, 94617711, 286574636, 875025121, 3931964183, 17811514229, 83204013462, 692178309352, 4578570288792, 27465149303522, 41578173908816
Offset: 0

Views

Author

Alexandre Wajnberg, Sep 18 2004

Keywords

Comments

May be considered as two sequences hidden in each other: the digits of Fibonacci are hidden in this sequence; the digits of this sequence are hidden in the Fibonacci. Same comment for A098080 and the counting numbers.

Crossrefs

Cf. A000045, A098080.

Formula

Write down the Fibonacci sequence and consider it as a unique succession of digits. Divide up into chunks of minimal length (and not beginning with 0) so that chunks are increasing numbers in order to form the slowest ever increasing sequences of slices (disregarding the number of digits) of the succession of the digits of the Fibonacci sequence.
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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